Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type
Abstract We prove the existence and uniqueness of a weighted pseudo asymptotically mild solution to the following class of abstract semilinear difference equations: u(n+1)=A∑k=−∞na(n−k)u(k+1)+∑k=−∞nb(n−k)f(k,u(k)),n∈Z, $$ u(n+1)= A \sum_{k=-\infty }^{n} a(n-k)u(k+1)+ \sum _{k=-\infty }^{n} b(n-k)f\b...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-06-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2189-y |
| _version_ | 1818283913076801536 |
|---|---|
| author | Valentin Keyantuo Carlos Lizama Silvia Rueda Mahamadi Warma |
| author_facet | Valentin Keyantuo Carlos Lizama Silvia Rueda Mahamadi Warma |
| author_sort | Valentin Keyantuo |
| collection | DOAJ |
| description | Abstract We prove the existence and uniqueness of a weighted pseudo asymptotically mild solution to the following class of abstract semilinear difference equations: u(n+1)=A∑k=−∞na(n−k)u(k+1)+∑k=−∞nb(n−k)f(k,u(k)),n∈Z, $$ u(n+1)= A \sum_{k=-\infty }^{n} a(n-k)u(k+1)+ \sum _{k=-\infty }^{n} b(n-k)f\bigl(k,u(k)\bigr),\quad n\in \mathbb{Z}, $$ where A is the generator of a resolvent sequence {S(n)}n∈N0 $\{S(n)\}_{n\in \mathbb{N}_{0}}$ of bounded and linear operators defined in a Banach space X, the sequences a,b $a, b$ are complex-valued, and f∈l1(Z×X,X) $f\in l^{1}( \mathbb{Z}\times X, X)$. |
| first_indexed | 2024-12-13T00:44:27Z |
| format | Article |
| id | doaj.art-bfed763bd73648419d2a8a45c3b2cffe |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T00:44:27Z |
| publishDate | 2019-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-bfed763bd73648419d2a8a45c3b2cffe2022-12-22T00:05:04ZengSpringerOpenAdvances in Difference Equations1687-18472019-06-012019112910.1186/s13662-019-2189-yAsymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution typeValentin Keyantuo0Carlos Lizama1Silvia Rueda2Mahamadi Warma3Department of Mathematics, Faculty of Natural Sciences, University of Puerto RicoDepartamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de ChileDepartamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de ChileDepartment of Mathematics, Faculty of Natural Sciences, University of Puerto RicoAbstract We prove the existence and uniqueness of a weighted pseudo asymptotically mild solution to the following class of abstract semilinear difference equations: u(n+1)=A∑k=−∞na(n−k)u(k+1)+∑k=−∞nb(n−k)f(k,u(k)),n∈Z, $$ u(n+1)= A \sum_{k=-\infty }^{n} a(n-k)u(k+1)+ \sum _{k=-\infty }^{n} b(n-k)f\bigl(k,u(k)\bigr),\quad n\in \mathbb{Z}, $$ where A is the generator of a resolvent sequence {S(n)}n∈N0 $\{S(n)\}_{n\in \mathbb{N}_{0}}$ of bounded and linear operators defined in a Banach space X, the sequences a,b $a, b$ are complex-valued, and f∈l1(Z×X,X) $f\in l^{1}( \mathbb{Z}\times X, X)$.http://link.springer.com/article/10.1186/s13662-019-2189-yWeighted pseudo asymptotically mild solutionsAbstract difference equationsResolvent sequences of operators |
| spellingShingle | Valentin Keyantuo Carlos Lizama Silvia Rueda Mahamadi Warma Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type Advances in Difference Equations Weighted pseudo asymptotically mild solutions Abstract difference equations Resolvent sequences of operators |
| title | Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type |
| title_full | Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type |
| title_fullStr | Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type |
| title_full_unstemmed | Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type |
| title_short | Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type |
| title_sort | asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type |
| topic | Weighted pseudo asymptotically mild solutions Abstract difference equations Resolvent sequences of operators |
| url | http://link.springer.com/article/10.1186/s13662-019-2189-y |
| work_keys_str_mv | AT valentinkeyantuo asymptoticbehaviorofmildsolutionsforaclassofabstractnonlineardifferenceequationsofconvolutiontype AT carloslizama asymptoticbehaviorofmildsolutionsforaclassofabstractnonlineardifferenceequationsofconvolutiontype AT silviarueda asymptoticbehaviorofmildsolutionsforaclassofabstractnonlineardifferenceequationsofconvolutiontype AT mahamadiwarma asymptoticbehaviorofmildsolutionsforaclassofabstractnonlineardifferenceequationsofconvolutiontype |